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09 Jan 2012, 22:05
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d = 83,521,y73/441,682,36y. In the expression above, the letter y represents a single digit from 0 to 9. Is d a decimal with exactly ten digits?
(1) The sum of all the digits in the numerator is not a multiple of 3.
(2) 33 is a factor of the denominator.
I have no idea how to solve this and what is he concept? Can someone please help?
(1) The sum of all the digits in the numerator is not a multiple of 3.
(2) 33 is a factor of the denominator.
I have no idea how to solve this and what is he concept? Can someone please help?
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16 Jan 2012, 18:59
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d = 83,521,y73/441,682,36y. In the expression above, the letter y represents a single digit from 0 to 9. Is d a decimal with exactly ten digits?
(1) The sum of all the digits in the numerator is not a multiple of 3. - not sufficient.
(2) 33 is a factor of the denominator. -> denominator is a factor of 3 and 11.
For denominator to be a factor of 11, difference of sum of alternate terms should be divisible by 11.
(16 + y) -18 should be divisible by 11
( y -2) should be divisible by 11
y can only be 2 as y can range from 0-9
so we know the numerator and denominator now and it should be sufficient to answer the question. no need to actually calculate. Hence B?
(1) The sum of all the digits in the numerator is not a multiple of 3. - not sufficient.
(2) 33 is a factor of the denominator. -> denominator is a factor of 3 and 11.
For denominator to be a factor of 11, difference of sum of alternate terms should be divisible by 11.
(16 + y) -18 should be divisible by 11
( y -2) should be divisible by 11
y can only be 2 as y can range from 0-9
so we know the numerator and denominator now and it should be sufficient to answer the question. no need to actually calculate. Hence B?
General Discussion
10 Jan 2012, 18:08
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Hi, there. I'm happy to put in my two cents here. 
I am unsure of the source of this question -- it's tagged as "Kaplan source", but I don't know what to make of that.
First of all, this question is way too technical, way too arcane, to appear on the GMAT math section. It's not the least bit realistic as a GMAT math question.
Second, for a variety of reasons, it seems a very poorly thought out question.
Because there are only ten possibilities for y, I went on Wolfram Alpha (https://www.wolframalpha.com/), which calculates answers to 56 decimal places in the blink of an eye, and I calculated all 10 ratios. The results are in the attached Word doc. Not surprisingly, all ten ratios are non-terminating decimals, so no possibility for y results in an decimal with exactly 10 decimal places. The two statements are completely irrelevant. Of course, I had to have one of the most sophisticated mathematical resources available to the public to do that, and during the actual GMAT, you will be limited to pencil and paper.
I will say: it's very hard to create a fraction that will have exactly ten decimal places. If a fraction has in the denominator a number with prime factors other than 2 or 5 --- and there's an infinity of prime numbers beyond those two --- then the fraction will be non-terminating, i.e. it will go on forever.
It was at least conceivable that, for some choice of y, the prime factors of the denominator other than 2 and 5 would cancel with prime factors in the numerator, and the result would be a terminating decimal, although in all likelihood even then, it would not terminate after exactly 10 digits. In any case, the point is moot, because for all values of y, the fraction never terminates, as expected.
Here is one GMAT Math idea related to this question that you definitely need to know: If a number is divisible by 3, then the sum of its digits is divisible by three. See my second posting on find-all-possible-values-of-x-advanced-question-125748.html to get a more detailed explanation of this.
Here is one math idea that, in an exceptionally rare case, you might need to know for the GMAT: If the only prime factors in the denominator of a fraction are 2 and/or 5, then when written as a decimal, the decimal terminates -- it comes to an end. If there are prime factors in the denominator of a fraction other than 2 and 5 that don't cancel with factors of the numerator, then when written as a decimal,the decimal does not terminate -- it goes on for ever.
Beyond that, I would say you can ignore this question.
Let me know if you have any questions about what I've said here.
Mike
I am unsure of the source of this question -- it's tagged as "Kaplan source", but I don't know what to make of that.
First of all, this question is way too technical, way too arcane, to appear on the GMAT math section. It's not the least bit realistic as a GMAT math question.
Second, for a variety of reasons, it seems a very poorly thought out question.
Because there are only ten possibilities for y, I went on Wolfram Alpha (https://www.wolframalpha.com/), which calculates answers to 56 decimal places in the blink of an eye, and I calculated all 10 ratios. The results are in the attached Word doc. Not surprisingly, all ten ratios are non-terminating decimals, so no possibility for y results in an decimal with exactly 10 decimal places. The two statements are completely irrelevant. Of course, I had to have one of the most sophisticated mathematical resources available to the public to do that, and during the actual GMAT, you will be limited to pencil and paper.
I will say: it's very hard to create a fraction that will have exactly ten decimal places. If a fraction has in the denominator a number with prime factors other than 2 or 5 --- and there's an infinity of prime numbers beyond those two --- then the fraction will be non-terminating, i.e. it will go on forever.
It was at least conceivable that, for some choice of y, the prime factors of the denominator other than 2 and 5 would cancel with prime factors in the numerator, and the result would be a terminating decimal, although in all likelihood even then, it would not terminate after exactly 10 digits. In any case, the point is moot, because for all values of y, the fraction never terminates, as expected.
Here is one GMAT Math idea related to this question that you definitely need to know: If a number is divisible by 3, then the sum of its digits is divisible by three. See my second posting on find-all-possible-values-of-x-advanced-question-125748.html to get a more detailed explanation of this.
Here is one math idea that, in an exceptionally rare case, you might need to know for the GMAT: If the only prime factors in the denominator of a fraction are 2 and/or 5, then when written as a decimal, the decimal terminates -- it comes to an end. If there are prime factors in the denominator of a fraction other than 2 and 5 that don't cancel with factors of the numerator, then when written as a decimal,the decimal does not terminate -- it goes on for ever.
Beyond that, I would say you can ignore this question.
Let me know if you have any questions about what I've said here.
Mike
Attachments
Chart for digit division question.docx [15.41 KiB]
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